And furthermore, objects in real world also have identities, which are distinct from their attributes. You aren't you because you have a certain name and date of birth, or a certain SSN. You're you because you're you. And we all intuitively know and understand this concept of identity. So any software that deals with real world entities has to reflect that concept, which is exactly what synthetic primary keys do.
And it might not be purely relational; but if purely relational model cannot handle this, then it's simply not a particularly useful model for most practical scenarios.
BTW, a pedantic argument could be made here that, ultimately, identity of physical objects is also data - you just need to go low-level enough (ultimately, the identity of any entity is its wavefunction) to see that. Of course, that ignores the practical aspects.